A possible instability to a glassy phase in type-II superfluids

U(1) nonlinear sigma model (NLSM) with a Berry phase term in D=d+1 dimension describes a zero-temperature partition function of d-dim type-II superfluids (SFs), where SF phase fluctuates in space r and time τ, while SF amplitude is constrained around a finite value by certain physical means. The Berry phase term along the time direction τ originates from a quantum-mechanical commutation relation between SF amplitude and phase. An ordered-disordered phase transition of the model is entirely driven by a spatial proliferation of vortex excitations (e.g. vortex loop in D=3, vortex hyper-sphere in D≥4), where the Berry phase term confers a complex phase factor upon the partition function with the vortex excitations, altering a nature of the disordered phase through an interference effect [1]. In this talk, we present a renormalization group (RG) theory of the model with D=4-ε, where a screening effect of smaller vortex hyper-spheres upon 1/|r|^D-2 Coulomb interaction among larger vortex hyper-spheres are systematically included according to a spirit of the ε expansion. By soloving RG equations in D=3 numerically, we argue a possible presence of a glassy phase next to the SF ordered phase in two spatial dimension. In the glassy phase, the exponential SF correlation time ξ_τ is divergent, while exponential correlation length ξ_r is finite.